Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations, so the description carries the full burden. It usefully discloses the return payload (side lengths, angles, perimeter, area, triangle classification flags, and theorem checks), which is real behavioral value. It fails to state that a rendered card is produced (only inferable from the locale param) or any side effects, so transparency is partial.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Two dense sentences with no filler, inputs listed before outputs. It is information-packed rather than rambling, though the output clause is a long run-on that slightly hurts scannability.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema, the description correctly spends its words describing return values, and it covers all four parameters including defaults. An absent annotation layer means a note on the rendered-card side effect would complete it, but nothing essential for calling the tool is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so the schema already documents shape, points, radius and locale. The description restates the shape enum, the point-array-per-shape constraint and the circle radius, adding only mild emphasis ("optional") beyond the schema. Baseline 3 is appropriate.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific resource (plane geometry) and enumerates the computed outputs, so an agent knows what the tool produces. The verb is soft ("interactive") and it never names sibling geometry tools like conic-sections or trig-lab, so differentiation is left to inference.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

"Use for middle-school geometry teaching" gives a target scenario, which is more than nothing. However, there is no when-not guidance and no routing against adjacent siblings (conic-sections, trig-lab, function-grapher), so selection still requires inference.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.